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Symposia on Turbulence in Liquids Chemical and Biochemical Engineering

01 Sep 1969

Two-Dimensional Laser-Doppler Velocimetry in Turbulent Flows Two-Dimensional Laser-Doppler Velocimetry in Turbulent Flows

N. E. Chatterton

R. D. Lewis

E. W. George

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Recommended Citation Recommended Citation Chatterton, N. E.; Lewis, R. D.; and George, E. W., "Two-Dimensional Laser-Doppler Velocimetry in Turbulent Flows" (1969). Symposia on Turbulence in Liquids. 42. https://scholarsmine.mst.edu/sotil/42

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TWO-DIMENSIONAL LASER-DOPPLER VELDCIMETKY

IN TURBULENT FIDWS*

N. E. C h a tte r to n , R. D. L ew is , and E. W. George Brown E n g in ee r in g Company, In c .H u n ts v i l le , Alabama

ABSTRACT

L o ca liz ed measurement o f the v e lo c i t y o f flow In f lu id s may be accom plished

by d e te c t in g the D opp ler s h i f t In frequ ency from coh eren t, monochromatic l ig h t

s c a tte red from m icrom eter s iz e d contam inant p a r t ic le s w ith in the f lo w . The

v e r s a t i l i t y o f a p p lic a t io n s o f th is te ch n iqu e , f i r s t used s e v e r a l y ea rs ago,

has been expanded by recen t re sea rch . The b a s ic geom etry o f measurement, in

which the s c a t te r e d energy is recombined w ith l ig h t en ergy a t the o r ig in a l

frequency on the fa c e o f the photocathode o f a pho toimil t i p l i e r tube, can be

rearranged in many a l t e r n a t iv e c o n fig u ra t io n s to meet the needs o f the e x p e r i­

m enter. By using a s in g le la s e r , a d d it io n a l arrangem ents are p o s s ib le fo r

o b ta in in g two- o r th ree -d im en s ion a l measurements o f v e lo c i t y components.

S e v e ra l d i f f e r e n t v e lo c im e te r s are d escr ib ed f o r making tw o-d im ensiona l flow

measurements, in c lu d in g both b a ck sca tte r and forward s c a t te r system s. E ffe c ts

o f f lo w system geom etr ies on c a p a b i l i t i e s f o r measuring s p e c i f i c components

are in v e s t ig a te d . E f fe c t s o f la s e r beam p o la r iz a t io n are d iscu ssed and con­

c lu s io n s reached on methods o f o p t im iz in g s ig n a l s tren g th in each o f two

o rth ogon a l measurement system s. R esu lts o f th e a p p lic a t io n o f a tw o-d im ensional

measurement system used fo r o b ta in in g v e lo c i t y p r o f i l e s in tu rb u len t f lo w in

a smooth w a lled fo u r - in ch d iam eter p ip e are p resen ted . O p era tin g a t a Reynolds

number o f about 1.1 x 10**, r e la t i v e tu rb u len t in t e n s i t ie s were measured in

the a x ia l d i r e c t io n and normal to th a t d i r e c t io n . Standard techn iques were

u t i l i z e d . A second readout system was employed to make a measurement o f th is

param eter w ith ou t the requirem ent o f adding s c a t t e r in g cen te rs to the flow .

INTRODUCTION

Measurement o f more than one component o f the v e lo c i t y in tu rbu len t f lu id

f lo w using the la s e r Doppler technique can be accom plished u s in g a number o f

d i f f e r e n t approaches. The o p t ic a l c o n f ig u ra t io n chosen is dependent upon the

in t e r r e la t io n s h ip between the v e lo c lm e te r and the flo w s y s te m -- ln v o lv in g the

g eo m etr ie s , the v e lo c i t y components d e s ir e d , and the c a p a b i l i t y to d e te c t

Che s ca tte red en e rg y . In th is paper, a b r i e f d e s c r ip t io n o f the op e ra tin g

p r in c ip le s o f the d e v ic e is g iv e n , fo llo w e d by d iscu ss ion s o f v e lo c lm e te r

systems em ploying s in g le In c id en t beam and d u a l in c id en t beams. A p p lic a t io n

o f a tw o-d im ensional v e lo c lm e te r is i l lu s t r a t e d w ith re s u lts from m asu re -

ments on a fo u r - in ch d iam eter p ipe w a te r f lo w system.

Resu lts o f measurement o f r e la t i v e tu rb u len t in t e n s it ie s a long the ax is

o f f lo w and app rox im ate ly normal to a d iam eter are g iv e n . A system i s d escribed

which can be u t i l i z e d w ith good r e s u lt s to measure turbu lence p a ra m te rs a t

low v e l o c i t i e s o r where a d d it io n o f s c a t t e r in g p a r t ic le s i s not p r a c t ic a l .

The la t t e r use is r e s t r ic t e d to systems where n a tu ra l contam inants a re present

in s u f f i c i e n t q u a n tity to produce s e v e r a l s ig n a ls p er second. The d e s c r ip t io n

o f the v e lo c lm e te r and r e s u lts o f i t s use p ro v id e a means o f d e te rm in in g

• kT h is work was p a r t ia l l y supported by the Navy Ship Research and Development

C en ter under the C enera l Hydrodynamics Research Program.

The f i r s t two au thors are P r in c ip a l Research P h y s ic is ts and the l a t t e r author is a P h y s ic is t w ith the P h ys ica l S c ien ces Research L a b o ra to r ie s o f Brown E n g in eer in g Company, In c .

f a c t o r s which must be s p e c i f i e d in o rd er to d es ign a system f o r a p a r t i c u la r

a p p l ic a t io n .

DESCRIPTION OF THE LASER DOPPI£R TECHNIQUE

The i n i t i a l use o f the D opp ler s h i f t in monochromatic, coherent ra d ia t i on

s c a t te r e d from p a r t ic le s suspended in a f lu id f lo w to d e t e c t v e l o c i t y was

rep o rted by Yeh and Cumnins in 1964.^ Subsequen tly , th is work was extended

and f i r s t a p p lied in a p r a c t ic a l instrument to measure lo c a l iz e d f low in

2 3 4gases and liq u id s a t these L a b o ra to r ie s . ’

Measurements in tu rbu len t f lo w have been repo rted by va r ious workers . In

o r d e r to sum aarize th a t w ork , i t i s necessary to d esc r ib e the p rocesses i n ­

v o lv e d in the d e te c t io n o f v e l o c i t y by the la s e r D opp ler te chnique. A

schem atic rep re s e n ta t io n o f a one-d imensional system i s shown in F igure 1.

F ig u re 1. Geometry o f One-D im ensional L aser Doppler V e lo c lm e te r

The D oppler eq u a tion , in terms o f the param eters shown in F igu re 2, is g iv en by

whe re

(1 )

( 2 )

i - 4 = (3 )

In these e x p re s s io n s , the w ave length o f the la s e r ra d ia t io n In the s c a t te r in g

medium is taken to be app rox im ate ly the same b e fo re and a f t e r s c a t te r in g and

I s rep resen ted by X ; ug and ^ a re u n it v e c to r s in the d i r e c t i o n o f s c a t t e r

and in the d i r e c t io n o f the In c id e n t beam r e s p e c t i v e l y , and v is the v e l o c i t y

o f the f lo w in the p lan e o f measurement. These v e c to r s a r e shown in F ig u re

2. U sin g the a n g le s d e fin ed in t h is f i g u r e , the s c a la r e q u a tio n f o r the

D opp ler s h i f t i s

f D 1 ST s in 1 s in ( y + ( * )

\ irs SCATTERED BEAM

) \ * “0 INCIDENT BEAM

V VELOCITY OF SCATTERER

F igu re 2. R e la t io n s h ip Between O r ig in a l and S c a t te r e d Wave V ec to r

The volume w ith in the s c a t t e r in g medium from which a measurement is made

is determ ined by the in t e r r e la t io n s h ip between the fo cu s in g o p t ic s and the

la s e r beam d iam eter and d is p e r s io n . I f d i f f r a c t i o n l im ite d o p t ic s a re em ploy­

ed , the sm a lles t d iam eter r e g io n th a t may be fo cu sed upon i s g iv en by

D - ( 5 )

where D ' i s the d ia m e te r o f the r e c e iv in g a p e r tu re and f i s the f o c a l len g th

o f the r e c e iv in g le n s . The le n g th o f the measurement volume is s e v e r a l tim es

th is d im ension . The in c id e n t beam i s focused to d im ensions app rox im atin g the

r e c e iv in g system c a p a b i l i t i e s . W h ile th is p ic tu r e i s c o n s id e ra b ly s im p l i f i e d ,

the measurement volume may be though t o f as b e in g produced by the in t e r s e c t io n

o f two c y l in d e r s . The measurement volume used h e re was 75 by 1,000 m icrom eters .

V ariou s methods have been used to make measurements in tu rb u len t f lo w .

G o ld s te in and Hagen^ rep o rted on use o f a spectrum a n a ly z e r as a readou t

method. Welch and Tonne** used a tim e c o r r e la t io n method to read ou t v e l o c i t y

p r o f i l e s a t a p o in t . L ew is , e t a l X used a p h a se -lo ck ed lo op to re co rd in s ta n ­

taneous v e l o c i t i e s . H u ffa k e r , F u l l e r , and Lawrence® rep o rted on the use o f

anoth er type frequ en cy t ra c k e r u s in g the ou tpu t o f a d is c r im in a to r to p ro v id e

the c o n t r o l s ig n a l f o r the feed b ack loop . A l l o f th e methods p r e v io u s ly

used depend on a more o r le s s con tinuous s ig n a l b e in g p resen t in o rd e r to

respond c o r r e c t ly . The readout techn iqu e d e s c r ib e d in th is paper does not

depend upon a near continuous s ig n a l being p re s e n t .

TWO-DIMENSIONAL GEOMETRIES

The ch o ice o f geom etry f o r the o p t ic a l system to be employed in making

a tw o-d im ensiona l measurement i s dependent upon th e measurement d i r e c t io n s

re q u ired and upon a number o f l im it a t io n s imposed by the v e lo c lm e te r system .

These l im ita t io n s must be determ in ed on the b a s is o f p a r t ic u la r c o n f ig u r a t io n s .

The s c a tte re d r a d ia t io n from a s in g le beam In c id e n t upon a d e s ir e d

volume may be d e te c te d a t two d i f f e r e n t p o s i t io n s in the fo rw ard s c a t t e r

d i r e c t io n to o b ta in a tw o -d im en s ion a l measurement ( s e e F ig u re 3 ) . A geom etry

a v a i la b le fo r o b ta in in g the v e l o c i t y component n e a r ly p a r a l l e l to the in c id e n t

beam is shown in F ig u re 4 . The f i r s t o f th ese s e t-u p s is d e s c r ib ed in the

s e c t io n o f th is paper e n t i t l e d Measurements o f T u rb u len t F low in a F ou r-In ch

P ip e . The l a t t e r s e t-u p re q u ire s th a t the r a d ia t io n in the b a c k s c a tte r d i r ­

e c t io n be s u f f i c i e n t to d e t e c t . F o r 0 .5 m icr om eter d iam e te r p o ly s ty r e n e la t e x

sp h eres , the r a t i o o f in t e n s i t i e s in the near fo rw a rd s c a t t e r d i r e c t io n

compared to in t e n s i t i e s in the f a r backward s c a t t e r d i r e c t i o n is n e a r ly 50

9to 1 a c co rd in g to M ie s c a t t e r in g th e o ry . I f the D op p le r spectrum i s spread

ou t due to tu rb u le n t f lo w , c o n s id e r a b ly g r e a t e r power must be used in the

in c id e n t beam to d e t e c t the s i g n a l . Experim ents in the fo u r - in c h d iam eter

p ip e f o r which d a ta are re p o r te d here In d ic a te d th a t a he lium -neon la s e r w ith

25 m i l l iw a t t ou tp u t was not s u f f i c i e n t to produce a u s e a b le s ig n a l a t the

Reynolds numbers o f f lo w used.

BS - BEAM SPLITTERPMT - PHOTOMULTIPLIER TUBEM - MIRRORL - LENSV - VELOCITY COMPONENT DETERMINED BY

THE SCATTERED BEAM IN THE X-Z PLANEV - VELOCITY COMPONENT DETERMINED BY

THE SCATTERED BEAM IN THE X-Y PLANEPMT 2

zr J V \ 7 . 5 ° ^ ‘ V.

[H \ / / V V: vcal. fp%,S He Ne

GAS LASER

NOTES:

1. Li,, M3, M,,, BSj, AND PMT2 ARE LOCATED IN THE X-Z PLANE.

2. L2 , M l M2 . BSi . ANO PMT, ARE LOCATED IN THE X-Y PLANE.

3. L lt L3. BS2, AND M s ARE LOCATED ON THE X AXIS.4. V2 IS LOCATED IN THE X-Z PLANE.5. V, IS LOCATED IN THE X-Y PLANE.

Figure 3. Two-Dimensional S in g le Inc ident Beam Veloclm eter

BS BEAM SPLITTER S ROTATING WHEEL VELOCITY SIMULATORPMT PHOTOMULTIPLIER TUBE V, VELOCITY COMPONENT DETERMINED BYM MIRROR THE FORWARD SCATTERED BEAML LENSES V2 VELOCITY COMPONENT DETERMINED BY

THE BACK SCATTERED BEAM

r ̂ , r------- 1t— He Ne { ^ i J , m I\GAS LASER \ 15° L- J"2V BSi Li ; 9(J«\s «t W T « s i

i * I i ii---------- J !____________________ i

Figure 4. Forward and Backscatter Veloclmeter System

19

Another system may be em ployed t o o b ta in o rth ogon a l components r e l a t i v e l y

e a s i l y . T h is system employs two In c id e n t beams to o b ta in two d ir e c t io n s o f

near forw ard s c a t te r r a d ia t io n . F ig u re 5 I l lu s t r a t e s such a system . A v e lo -

c im e te r con stru cted w ith th is geom etry o f f e r s symmetry o f measured v e lo c i t y

components w ith r e s p e c t to the f lo w a x is geom etry , which m ight be a c o n s id e r ­

ab le a s s e t in s o fa r as " t r a c k in g " i s concerned as w i l l be seen . The components

thus measured, how ever, a re not those o f most in t e r e s t fo r tu rbu len t f lo w in

most channels . In a d d it io n , Beam 1 can heterodyne w ith s ca tte re d en ergy from

Beam 2 and v ic e ve rsa and th e s c a t te r e d beams can heterodyne w ith each o th e r .

10An e x te n s iv e a n a ly s is o f th is system is found e lsew h ere .

When nx>re than one component o f v e lo c i t y in a system is measured, e f f e c t s

o f the p o la r iz a t io n o f the in c id e n t and s c a t te r e d beams become more d i f f i c u l t

F igu re 6. E f fe c t s o f P o la r iz a t io n R o ta tion on Received S ign a l

F igu re 5. Two-D im ensional Tw in In c id e n t Beam V e lo c im e te r

to a llo w fo r in s e t t in g up the geom etry o f the v e lo c im e te r . An experim ent

was perform ed to f in d ways o f m in im izing p o la r iz a t io n e f f e c t s . The p lane o f

p o la r iz a t io n o f the output o f a Model 124 S p ec tra -P h ys ics la s e r was ro ta ted

by us ing an accesso ry p o la r iz a t io n r o ta to r . A th in mylar wheel was used as

a flow s im u la tor to produce the data shown in F igu re 6. The plane o f p o la r iz a ­

t io n was va r ied from v e r t i c a l ( 0 ° ) to h o r iz o n ta l (9 0 ° ) . Curves 1 and 2 were

ob ta in ed by ob se rv in g the in t e n s it y o f the heterodyne s ign a l on a H ew le tt-

Packard Model 8551 A spectrum an a ly ze r u s in g the back sca tte r and forward

s c a t te r systems o f F igu re 4 . These systems were mounted in the h o r iz o n ta l

p lan e . In the b a ck sca tte r system , a v a r ia t io n o f 2 .5 d e c ib e ls re su lted from

the r o ta t io n o f the p o la r iz a t io n p lan e . In c o n tra s t , the forward s c a t te r

system produced a s ign a l l e v e l th a t v a r ied over 9 d e c ib e ls .

These losses are in cu rred a t r e f l e c t in g su rfa ces w ith in the system . A

d i e l e c t r i c su rface (such as a g la s s beam s p l i t t e r ) w i l l change the plane o f

p o la r iz a t io n o f the r e f le c t e d beam from the o r ig in a l plane excep t under s p e c i f i c

c o n d it io n s ; i f the plane o f p o la r iz a t io n i s p erpen d icu la r to the p lane con­

ta in in g the In c id en t and r e f l e c t i v e beam o r i f the in c id en t beam s t r ik e s the

r e f l e c t in g su rface near the norm al, then the p lane o f p o la r iz a t io n is le a s t

a f f e c t e d . R e f le c t io n from m e ta l l ic s u r fa c e s , in g e n e ra l, reduces the in te n s ity

in a g iv en plane o f p o la r iz a t io n by e l l l p t i c a l l y p o la r iz in g the r e f le c t e d

beam. A rranging the system to p ro v id e near normal in c idence on w t a l l l c r e ­

f l e c t o r s a lso reduces th is lo s s . Curves 3 and 4 were ob ta in ed w ith two e x ­

p er im en ta l systems which were designed w ith no a n g le o f in c id en ce g r e a te r

than 25 °. The maxinum s ig n a l lo s s experien ced was 3 1/2 d e c ib e ls . A two-

d im ensional system must use these p r in c ip le s i f the losses are to be kept to

a minimum. The d e s i r a b i l i t y o f th is is r e a d ily apparent in reducing cost o f

the la s e r to be used and in k eep ing the bu lk o f the system as low as p r a c t ic a l .

MEASUREMENTS IN TURBULENT FLOW IN A FOUR-INCH PIPE

A system s im i la r to th a t shown in F igu re 3 was se t up on a 4 -in ch ou ts id e

d iam eter g la s s p ip e flow system . Two modes o f o p e ra tion were attem pted . In

ord e r to b e t t e r ob serve the component o f v e lo c i t y in the z - d ir e c t io n (d e f in e d

in F igu re 3 ) , a d ir e c t io n normal to the a x is o f the p ip e , m o d ific a t io n s were

made in the p ro cess in g c i r c u i t r y f o r s ig n a ls cen tered about ze ro v e lo c i t y .

F i r s t , the re fe re n c e beam was genera ted by passing the la s e r beam through

an a c o u s t ic - o p t ic a l c e l l to s h i f t the frequency o f a p o r t io n o f the beam by

30 m egahertz. S econd ly , the re fe ren c e beam was passed around the flow system

in o rd e r to m in im ize am plitude v a r ia t io n s . The heterodyne s ig n a l produced

by th is system is cen tered about 30 megahertz ra th e r than ze ro frequency.

Th is procedure makes i t p o s s ib le to view low v e lo c i t y sp ec tra on a spectrum

a n a ly ze r w ithou t being trou b led by the z e ro frequency s ig n a l p resent to some

degree in a l l spectrum a n a ly ze rs and, more Im portant, to g e t r id o f the low

frequ en cy noise genera ted in the la s e r . Mode in te ra c t io n in the la s e r can

c rea te spurious s ig n a ls o f narrow bandwidth a t low fre q u en c ie s . Once a

s ig n a l cen tered about 30 m egahertz is ob ta in ed , i t may be mixed w ith a con­

s ta n t frequ en cy ra d io frequency s ig n a l to lo ca te the frequency correspond ing

to ze ro v e lo c i t y a t any p o s i t io n in the spectrum d e s ire d . A b lock diagram

o f th is apparatus is shown in F igu re 7.

The flow system used is a c lo sed lo o p , fou r-in ch d iam eter u n it . The

loop is d r iv en by a 60-horsepower a c to r d r iv in g a pump ra ted a t 1100 gal/m in

a t a t o t a l head r is e o f 150 f e e t o f l iq u id at 1700 rpm. Bulk flow ra te s

through the tube are measured w ith a p r o p e l le r - ty p e vo lu m etr ic flow m eter lo ca ted

in the 4 -ln ch d iam eter l in e on the su c tion s ide o f the pump. The v e lo c im e te r

measurements were made in a g la s s -w a lle d sec tion o f the system . The system

is v ib r a t io n Is o la te d from the surroundings by rubber pads on the supports

and a f l e x i b l e cou p lin g to the pump. A vacuum system was used to remove

LASERBEAM

H3

F ig u re 7. Double C on vers ion H eterodyne System

d is s o lv e d a i r from the w ater in the loop so as to p reven t bubble fo rm a tion .

6The u lt im a te Reynolds number o f the system i s 1 .8 x 10 . The f lo w system

heats up d u r in g runs because o f f r i c t i o n . Measurements u t i l i z e d here were

made o v e r a w a te r tem perature range o f 95 to 105°F co rresp on d in g to a Reynolds

number range o f 1.12+0.06 x 10^ a t the v e lo c i t y used . The v e lo c im e te r r e ­

c e iv in g a p e r tu re was s e t to produce a read ab le s ig n a l a t a l l measurement

p o s it io n s w ith in the tube. An e x c e p t io n to these o p e ra t in g co n d it io n s was

in measurements w ith the doub le con ve rs ion h e terodyne system , where the

len g th o f tim e necessary to make the measurement extended the o p e ra t in g

tem peratures t o between 90 and 114°F.

Two fa c t o r s a s so c ia ted w ith o p t ic a l system param eters have been c i t e d

as cau s in g l i n e broaden ing o f the D opp ler s ig n a l . Exam ination o f Equation 4

fo r th e D opp ler frequency shows that i f s c a t te r e d r a d ia t io n is r e c e iv ed o v e r

a f i n i t e an gu la r a p e rtu re , the D oppler spectrum o f the r a d ia t io n i s broadened

a c c o rd in g ly . D i f f e r e n t ia t io n o f Equation 4 w ith re sp e c t to © and * y ie ld s

dfD - j j i sin f cos ('*' + f ) ♦ \ cos 1 sln + f l j M

+ s in ^ cos ( « + e ) dw ( . ( 6 )

2 )For a system such as th a t shown in F igu re 6 , f * 90° and the f r a c t io n a l s h i f t is

u tn 1 a—— * c o t 0 d© - — tan — d y . ( 7 )f D 2 2

The s ig n a l produced by a s c a t t e r e r p a ss in g through the measurement volume is

in th e form o f a p u lse . The tim e o f o ccu rren ce o f the p u lse is

t - ( 6 )n

where D is a d im ension o f the measurement volume such as d e fin e d in Equation 5

and v^ is the v e lo c i t y component across th a t d im ension . The spectrum o f such

a p u lse has frequ en cy spread o f

( 9 )

I t has been p o in ted ou t that f o r d i f f r a c t i o n l im ite d o p t i c s , the frequency

spread caused by the spread in s c a t te r in g a n g le s observed should be rero f o r

rays r e c e iv e d from the bundle a t the focu s o f the o p t ic a l system . The

magnitude o f p o s s ib le v e lo c i t y spread in the system used here may be es tim a ted

by ta k in g a v a lu e o f about 0 - 15° approxim ate mean v e r t i c a l component measure-

3merit a n g le , d© * (3 nan a p e r tu re a t a d is ta n c e o f 140 mm), dy * 0 ( f o r

purposes o f th is o rd e r o f m agnitude e s t im a te ) to g e t from E quation 7

— 5 - 0.08 . (1 0 )D

T h is va lu e may not be ob served in p r a c t ic e . In a d d it io n to the reason

fo r a narrow er spectrum g iv e n ab ove , the h e te ro d yn in g e f f i c i e n c y a t the

p h o t o m i l t ip l l e r is dependent on how n e a r ly c o l in e a r the s c a t t e r e r and r e f e r ­

ence beams a r e , and the beam I n t e n s i t i e s drop o f f a t the edges o f the s c a t t e r ­

in g vo lume.

The frequ en cy spread in the measured v e r t i c a l component i s a ls o a f fe c t e d

by in t r o d u c t io n o f a component o f th e a x ia l v e l o c i t y in to the measurement by

the f i n i t e a n g le o f a ccep tan ce in the system . A t the c e n te r o f the f lo w , under

the same c o n d it io n s c i t e d above to c a lc u la t e maximum frequ en cy spread due to

the e f f e c t o f f i n i t e a p e rtu re on the measurement o f the d e s ir e d component,

the maxitmim freq u en cy component in trodu ced in to the measurement due to th is

e f f e c t may be c a lc u la te d from E qu a tion 4 . I f the system i s c a r e fu l ly a lig n e d

to be sym m etrica l abou t a component normal t o the a x ia l f lo w , an ang le o f

e3

280deg ( 11 )

is used in the e q u a t io n . T h is y ie ld s

d fD “ ±195 k i lo h e r t z (1 2 )

where the mean D op p le r frequ en cy produced by the v e l o c i t y component a lon g the

system a x is i s 3 .60 m egahertz.

Using a m ylar w heel a t the measurement p o in t , the frequ en cy spread due

to a l l fa c t o r s m entioned here amounts to

—p ST o .04 . ( 13)D

Wave t ra in s from the wheel appear to ex tend o v e r a lo n g e r p e r io d o f time than

would be exp ec ted from a p a r t i c l e t r a v e r s in g the measurement volum e. For

th is reason , the frequ en cy spread due to pu lse broaden ing would be expected

to be le s s than w ith p a r t ic u la t e m a te r ia l . A nother measurement was made w ith

the m ylar w heel p la ced so th a t the v e lo c i t y was a p p rox im a te ly normal to the

p lane c o n ta in in g the s c a tte re d and r e fe r e n c e beams. An e f f e c t i v e s c a t te r in g

ang le o f

© « 0 .6 2 deg ( 14)

was computed on the b a s is o f an ob served D opp ler mean frequ en cy o f 130 k i l o h e r t z .

The frequ en cy spread was 70 k i l o h e r t z . Th is p ro v id e s an upper l im i t fo r the

pu lse b roaden ing f o r the w h ee l, s in ce the an gu la r ap e rtu re should produce the

frequ ency speed n o ted . Computation o f th is frequ en cy spread y ie ld s

f D - +70 k i lo h e r t z (1 5 )

which i s doub le the measured v a lu e . H owever, a t such a sm all e f f e c t i v e

s c a t t e r in g a n g le sm all e r r o r s in w heel p o s i t io n produce la r g e e r r o r s in th is

measurement. In com putations o f the frequ en cy spread due to the angu lar

a p e r tu re , the va lu e computed from the above measurements was used:

d© - 0.762 deg . ( 16)

Th is va lu e i s 60 p e rc en t o f the va lu e coaqxited from the a p e rtu re s iz e .

The p u lse b roaden in g o f the spectrum may be es tim a ted from Equations 8

and 9 . Near the a x is o f the tube, the sa in f lo w v e lo c i t y i s la r g e enough

w ith re sp e c t to the tu rb u len t v e l o c i t y tha t the time fo r a p a r t i c l e to go

a cross the beam may be e s tlam ted from the mean v e l o c i t y a lo n e . T h is holds

fo r measurements normal to the a x is o f the system as w e l l , s in c e v e lo c i t i e s

21

In th e * * d ir e c t io n s arc s a u l l compared to Bean a x ia l v e l o c i t y . W ith a 75-

m icrom eter w ide baas and a peak aean v e lo c i t y o f 8 .65 m eters p e r second , the

frequ en cy spread I s

f t f t - 115 k i l o h e r t z (1 7 )

T h is spread I s dependent on the p o s i t io n w ith in the f lo w , o f cou rse .

The fo u r - in c h d iam eter f lo w system was used to study the I n t e r r e la t io n ­

sh ip between system g eom etr ies and the fa c to r s a f f e c t in g the D opp ler f r e ­

quency ou tp u t. The h o r iz o n ta l component o f v e lo c i t y measured was p a r a l l e l to

the tube a x is w h ile the v e lo c i t y conq>onent measured normal to th is a x is was

s l i g h t l y o f f the v e r t i c a l . W ith a f ix e d r e c e iv e r geom etry , the re s u lta n t

measurement d i r e c t io n a t th re e p o s it io n s w ith in the tube Is shown In F igu re 8 .

As can be s een , the s c a t t e r in g an g le changes as the measurement volume Is

moved In from the edge o f the tube. The s c a t te r in g an g le must be determ ined

a t each p o in t and used to c a lc u la t e the con vers ion fa c t o r from frequ en cy to

v e l o c i t y . In th is system , the v e lo c lm e te r geom etry remains f ix e d du rin g the

scan . The v e r t i c a l component may be d i r e c t l y measured, but a system o f that

typ e would r e q u ire rea lign m en t a t each measurement p o s i t io n . S ince the s c a t t e r ­

ed energy In the h o r iz o n ta l component system i s con ta in ed w ith in a p r in c ip a l

p la n e , the s c a t t e r in g an g le remains fix e d d u rin g scan . Th is component was

measured a t a s l i g h t angle t o the a x ia l d i r e c t io n .

3. C • POSITION (0.00)83°19'

F igu re 8. V a ria tion o f Measured N e a r -V e rt ic a l Component With Radial Position

Measurements In a tube with these components saist take account o f the

d if fe r e n t "tra c k in g " rates o f the measurement volumes. Figure 9 shows the

re la t io n sh ip between the distance the velocim eter Is traversed and the d is ­

tance from the edge o f the tube the measurement volume la moved. The two

measurement volumes do not move at the same rate as the system la traversed,

and, In f a c t , the near v e r t ic a l component measurement v o lu v la traversed

n o n - l in e a r ly w ith re sp e c t to the system m otion . The two volum es, i f s e t to

c o in c id e a t the edge o f the tube, w i l l be separa ted by 0 .7 in ch a t the center .

By making the volum es c o in c id e n t a qu arter o f the way across the tube, the

maxlaim d r r o r Is about 0 .3 In ch , which i s s t i l l too la r g e f o r any c o r r e l a t i o n -

typ e measurement. Sim ultaneous measurements o f these two components a t the

same measurement p o s i t io n r e q u ir e s a complex t ra v e r s in g scheme, w ith the two

component systems t r a v e r s in g a t d i f f e r e n t r a t e s .

The mean v e l o c i t y p r o f i l e was measured from a spectrum a n a ly z e r ou tpu t.

The r e s u lts o f th is measurement a re shown in F igu re 10. The mean v e lo c i t y

a t the c e n te r o f the tube was 8 .65 meters p e r second as measured by the

v e lo c lm e te r as compared t o a v e lo c i t y o f 8 .58 m eters per second computed

from the v o lu m e tr ic measurement o f the flow m ete r .

A l l d a ta u s in g a spectrum a n a ly ze r ou tp u t was ob ta in ed by adding 0.500

m icrom eter p o ly s ty re n e la t e x spheres to the w a te r in the system . Measure-

ments near the w a l l w ith th e apparatus are n o t expected to have much s i g n i ­

f ic a n c e because o f the len g th o f the measurement volume a long the r e f e r en c e

beam— about 1 m il l im e te r t o the h a l f power p o in ts . At po in ts f a r from the

w a l l , the s ig n i f ic a n c e o f the l in e broaden ing fa c to r s can be e s t im a ted . At

th e c en te r o f the tube, by us in g mean v e l o c i t y o f 8.65 meters per second, the

h o r iz o n ta l component y ie ld s

0.043 (1 8 )

1/1

s

0-0 0.4 0.8 1.2 1.6 2.0 2.4 2.f

DISTANCE FR0H EDGE OF TUBE (in)

F igure 9. Measurement Volume P o s ition "Tracking" o f Velocim eter Motion

■ —

iLEGEND:

/

OLDV DATA□ NIKURADSE, 1.1 * 10s NRe NOTES:1 . V - VELOCITY IN AXIAL

DIRECTION2. VM x * VELOCITY IN AXIAL

DIRECTION AT TUBE’S CENTER

h1 —0.0 0.2 0.4 0.6 0.8 1.0

FRACTIONAL PIPE RADIUS, r/R

Figure 10. Mean V e loc ity P ro f i le In 4-1 neh Tube

1.2

22

and Che near ve r tic a l component yields

AVv“ - °-030 (1 9 )

xmax

The va lu es are computed from measurement o f o n e -h a l f the freq u en cy spread b e ­

tween h a l f am p litu de p o in ts . C o r r e c t iv e fa c t o r s th a t can be a p p lie d have

been d iscu ssed a b o ve . These In c lu d e the freq u en cy spread due to p u lse w id th

from Equation 17

- 115 k i l o h e r t z (2 0 )

and the frequ en cy spread due to the an gu la r a p e r tu re from E qu a tion 13

d f = 140 k i l o h e r t z (2 1 )°H

fo r the h o r iz o n ta l component and from the an gu la r a p e rtu re computed from

Equations 13 and 7

d fp = 50 k i l o h e r t z (2 2 )

f o r the v e r t i c a l component.

These c o r r e c t iv e fa c to r s a re a p p lie d on the b a s is o f assum ing each f r e ­

quency spread I s an independent Gaussian d is t r ib u t io n . The c o r r e c te d spread

w i l l be 2 2 2 *

(t^ - ) ■ r ir |b “-) - ( l A ) - ( i £ - ) ] «»>V xmax/ l v xmax/ V xmax/ V xmax/ Jc o r r

where the o n e -h a l f fa c to r s in the p u lse and a n gu la r a p e r tu re terms e n te r b e ­

cause the d e s ir e d spread Is the r o o t mean square d e v ia t io n from the mean. The

frequ en cy spreads must be c o n ve rted to e q u iv a le n t v e l o c i t y spreads to use th is

e q u a t io n , Av t co rresp on d in g to the pu lse b road en in g term , d v co rresp on d in g to

the an gu la r a p e r tu re term and a v to the observed sp read . By u s in g va lu es from

Equations 18 and 19, con verted to v e l o c i t i e s , the c o r r e c te d va lu es become

( - T Y 1----- ) - 0 .0335 (2 4 )V <v>xmax'

c o r r

V <av v----- 1 “ 0 .028 . (2 5 )

V ( v ) xmax J c o r r

The angu lar a p e rtu re c o r r e c t io n fa c to r s i g n i f i c a n t l y a f f e c t s the h o r iz o n ta l

component, but not the v e r t i c a l . The pu lse c o r r e c t io n f a c t o r s i g n i f i c a n t l y

a f f e c t s bo th . The p e rcen t c o r r e c t io n produced by these term s la a t the moat

23 p e rc e n t. As one moves toward the edge o f the tu b e , the an gu la r ap e rtu re

c o r r e c t io n fa c t o r becomes leaa Im portan t f o r the h o r iz o n ta l component and

remains about the same fo r the v e r t i c a l component. The p u lse c o r r e c t io n

fa c t o r becomes le s s lo iportan t as th e edge o f the tube la approached . The

c o r r e c te d cu rves o f r e la t i v e tu rb u le n t In t e n s i t i e s a re p lo t t e d In F igu re 11.

The frequ en cy sp reads * f y and A fj j w ere ob ta in ed by om asurlng between +3rr p o in ts

on the Gaussian shaped spectrum a n a ly z e r t r a c e s .

The two components o f r e la t iv e turbulenc In ten s ity measured here were

14compared to the re s u lt s o f L au fe r presented In H lnze. L au fe r s d a ta , taken

w ith hot-w ire anemometers, were obtained a t a s l ig h t ly sm a lle r Reynold 's

number than here. The agreement between the data i s good except that the v e r t i ­

c a l component measured appeared more constant w ith rad ia l d istance In the

current measurement. A lso , near the w e ll , the la s e r veloclm eter measured h o r i ­

zon ta l component Increased at a g re a te r d istance from the w a ll than did the

previous re s u lt . As explained e a r l i e r , the measurement volume was la rg e s t

a long th is ax is and w ith th is p a r t ic u la r se t-up one could not expect to get the

re so lu tio n requ ired to s u t u r e tu rbu len t In te n s it ie s at the w a ll.

The second aaode o f operation described above was used w ith the v e r t ic a l

0.161--------------------------------- -------------------------------------------------------------------------------LEGEND:

8 MEASURED HORIZONTAL COMPONENT ICASURED VERTICAL COMPONENT

A VERTICAL COMPONENT - LAUFER (see Note)»; n , , _____________ □ HORIZONTAL COMPONENT - LAUFER (see Note)5; j A MEASUREMENT TAKEN WITH APPARATUS OF£ I FIGURE 7 - VERTICAL COMPONENT

- ----------1------ NOTE: LAUFER DATA TAKEN AT Re * 5 « 105.£ v i DATA IS REPRODUCED FROM HINZE1*.

2 0.08 ---------------------- ------------------1-----------| ^ U i i - | _

0.00 _____ I____________I____________1______1____________ I______I_____0.0 0.2 0.4 0.6 0.8 1.0

r/R

F igu re 11. R e la t iv e Turbulent In te n s it ie s

component at one po in t a t the cen ter o f the tube. The r e la t iv e tu rbu len t in ­

ten s ity measured in th is manner was

/ Av „ \[ - — — j = 0.025 . (26 )

v / co rr

A p lo t o f the counting ra te versus frequency i s shown in F ig u re 12. A

Gaussian d is t r ib u t io n has been p lo tted w ith the same root mean square d e v ia t io n

using the same mean. The no ise le v e l Ind icated on the p lo t was o b ta in ed by

b lock ing the sc a tte red beam and observ ing the cou n t. The s ig n i f i c a n c e o f the

measurement Is that the count was made w ith no a r t i f i c i a l contam inants added

to the w ater. A spectrum a n a ly z e r output o f th is s ign a l could not be used to

determine the frequency spread because o f the sm all number o f s ig n a ls b e in g

produced.

An am biguity Is present In app ly ing the pu lse width co rrec tion fa c to r

when a r t i f i c i a l contaminants a re added to the system. In such a ca se , more

than one p a r t ic le Is present w ith in the measurement volume at any one time

and the resu ltan t pulse t ra in appears to o ften exceed the number o f cyc les

expected from the dimensions o f the volume. The system w ith no a r t i f i c i a l

contaminants p resent Is such that In d iv id u a l p a r t ic le s produce the heterodyne

s ig n a ls rece ived .

1.600 -------------------------------------------------------------------------------------------------------------- ---------NOTES:TU-7 ---------- ---------------------- -----TUBE CENTER v-v• - 15.75 / \

, 1,200 V/z » 1.75 «/mHz ----4---V-i---------- ----------------m \ 0-707" LEGEND: / POINT•C ----MEASURED / 1'UJ ----GAUSSIAN DISTRIBUTION / l

i -------Prrrrr-___ __ _ _______ __ ___ ___ _________ _____ __________ NOISE

ol Z L I 1 . 1 1 1 1 , LEVEL0.00 0.40 0.80 1.20 1.60 2.00 2.40

FREQUENCY (mHz)

F igu re 12. Counting Rate as a Function o f Frequency

23

The techn ique as p r e s e n t ly used is cumbersome, w itn essed by the fa c t th a t

w ith th is f lo w system on ly one data p o in t cou ld be obta ined w ith a reasonab le

exp en d itu re o f tim e. The t o t a l len g th o f tim e u t i l i z e d in c o l l e c t in g data

used In the p lo t te d spectrum shape was ap p rox im a te ly one and a h a l f hours. In

a d d it io n , two shut-downs were n ecessa ry to l e t the w a ter c o o l to s ta y w ith in

the tem perature o p e ra t in g range s p e c i f ie d e a r l i e r . During th is tim e , contaminant

l e v e l had to remain constan t and no a i r bubbles cou ld be a llow ed to form .

A d d it io n a l experim ents are planned to decrease the length o f time requ ired f o r

a measurement and to e x p lo re any a d d it io n a l l im ita t io n s .

CONCLUSIONS

Tw o-dim ensional measurements o f tu rbu lence parameters in f lu id f lo w us ing

a la s e r D opp ler v e lo c im e te r req u ire d e ta i le d a n a ly s is o f v e lo c im e te r - f lo w

system in te r a c t io n s to produce m ean ingfu l r e s u lt s . Frequency broaden ing o f

the s ig n a l is produced by both p u lse w id th and angu lar apertu re e f f e c t s . W h ile

both fa c to r s can be c o n t r o l le d , o th e r c o n s id e ra t io n s en te r in to the c a p a b i l i t y

to va ry them. A sm a lle r apertu re s i z e produces a reduced s ig n a l l e v e l . In

th is ca se , the s ig n a l l e v e l was ad ju s ted to the minimum co n s is ten t w ith r e l ia b le

da ta ta k in g . A sm a lle r measurement volume can be produced, but th is req u ires

in creased apertu re s iz e s and in c rea ses frequ ency spread due to pu lse w id th .

Measurements may be made in la r g e systems where i t is im p ra c t ic a l to add

s c a t t e r in g p a r t ic le s so lon g as c o n d it io n s w ith in the f lu id remain constan t

o v e r the measurement tim e. Low frequ en cy la s e r n o is e and low frequ ency char­

a c t e r i s t i c s o f e le c t r o n ic readout systems can be circum vented in low v e lo c i t y

tu rb u len t f lo w measurements by use o f a dua l conversion heterodyne system .

R esu lts comparable to more con ven tion a l methods are ob ta in a b le w ith p roper

a t t e n t io n to the o p e ra t in g param eters.

SYMBOLS

f DDoppler frequency

KS s c a t te r in g frequency

*o in c id en t frequency

Us . Uo u n it v e c to rs

^ w ave len g th in s c a t t e r in g medium

v f lu id f lo w v e lo c i t y

D sm a lle s t d iam eter o f beam

f f o c a l len g th o f r e c e iv in g lens

D' r e c e iv in g apertu re

0 , tl/ ang les d e fin ed in f ig u r e 2

t tim e o f s c a t t e r in g pulse

vn v e l o c i t y in p lane normal to s ca tte red beam

A f frequ en cy spread o f pu lse

v n h o r iz o n ta l v e lo c i t y component

v v v e r t i c a l v e lo c i t y component

vx max c e n te r l in e v e lo c i t y

REFERENCES

1. Yeh, Y .,and Cunmins, H. F . , App. Phy, L e t t e r s , 4 , 176 (1 9 6 4 ).

2. Foreman, J . W.2 , 77, (1 9 6 5 ).

. , J r . , George , F. W ., and L ew is , R. D., , App. Phy. L e t t e r s

3. Foreman, J . W.• » J r . * e t a l , P ro c . IEEE, 54. 424-425 ( 1966).

4 . Foreman, J . w.• » J r . , e t a l , IEEE Journal o f Quantum E le c t r o n ic s ,Q E -l, 260- 266 (1966)

5. G o ld s te in , R. J . , and Hagen, W. F . , Phys. F lu id s ,10, 1349-1352 ( 1967).

6. W elch , N. E .,an d Toirnne, J . , AIAA Paper No. 67-179, AIAA 5th Aerospace S c ien ces M ee tin g , New York , New York , January 23-26, 1967.

7. L ew is , R. D . , e t a l , Phys F lu id s , 11, 433-435 (1 9 6 8 ).

8 . H u ffa k e r , Robert M ., F u l le r , C. E . , and Lawrence, T. R . , paper presen ted a t In t e r n a t io n a l Autom otive E n g in eer in g Congress, D e t r o i t , M ich igan , January 13-17, 1969.

9 . Department o f Coiimerce, N a t io n a l Bureau o f S tandards, Tab les o f S c a t te r in g Functions f o r S p h er ica l P a r t i c l e s , A p p lied Mathematics S e r ie s 4 , January 1949.

10. L ew is , R. D . , e t a l , In v e s t ig a t io n o f Two-Dimensional Flow Measurements Using the Laser D oppler Techn ique, Brown E ng in eerin g Company, I n c . , T ech n ica l Note AST-285, H u n ts v i l le , Alabama, December 1968.

11. Cunmins, H. F .,and K n ab le , N. , P roc . IEEE. 51, 1246 ( 1963).

12. P ik e , E. R . , e t a l , J . S e t. I n s t r . . 1. 727-730 ( 1968).

13. Ross, M. , L a ser R e c e iv e r s . John W iley and Sons, In c .,N ew York, 1966

14. H ln ze , J . 0 . , Turbu lence, An In tro d u c t io n to I t s Mechanism and T h eo ry , M cG raw -H ill Book Company, New York, 1959.

24